Abstract: This paper focuses on numerical simulation of the long-wave short-wave interaction equation. Two fourth-order compact finite difference schemes are proposed and proved to preserve the total mass and energy in the discrete sense. Numerical results show the good stability of the schemes and fourth-order and second-order convergence of the numerical solutions in space and time, respectively. Simulation results also show that the schemes preserve well the total mass and energy.

Key words: long-wave short-wave interaction equation, compact finite difference scheme, mass conservation law, energy conservation law